A so-called "incentive contract " is a linear payment schedule, where the buyer pays a fixed fee plus some proportion of audited project cost. That remaining proportion of project cost borne by the seller is called the "sharing ratio. " A higher sharing ratio creates more incentive to reduce costs. But it also makes the agent bear more cost un-certainty, requiring as compensation a greater fixed fee. The tradeoff between incen-tives and risk in determining the sharing ratio of an efficient contract is the central theme of the present paper. A formula is derived that shows how the optimal sharing ratio depends on such features as uncertainty, risk aversion, and the contractor's ability to control costs. Some numerical examples are calculated from the area of defense contracting. SUMMARY This paper analyzes the widely used "incentive contract"—a linear payment schedule where the buyer pays a fixed fee plus some proportion of project cost. The remaining proportion of project cost borne by the seller is usually called the "sharing ratio. " A higher

I. Introduction, 156. — II. A formulation of the problem, 156. — III. What is net national product? 159. — IV. Proof of the main proposition, 160. — V. Unanticipated technological change: an application, 161.

I. Introduction, 262. — II. The economic environment, 263. — III. Mechanics of planning, 265. — IV. Material reserves, 266. — V. Plan formulation and material balances. 267. — VI. Effects of uncertainty, 268. — VII. Plan execution and the costs of incorrect planning, 270. — VIII. Short- and long-term plans, 272. — IX. Optimal planning and dynamics programming, 273. — X. Sensitivity analysis, 276. — XI. Concluding remarks, 278. — Appendix: Proof of the form of an optimal policy, 278.

This paper is about the economic theory of biodiversity preservation. A cost-effectiveness methodology is constructed, which results in a ranking criterion sufficiently operational to be useful in suggesting what to look at when determining actual conservation priorities. The formula is firmly rooted in a mathematically rigorous optimization framework, so that its theoretical underpinnings are clear. The underlying model, called the 'Noah's Ark Problem, ' is intended to be a kind of canonical form that hones down to its analytical essence the problem of best preserving diversity under a limited budget constraint.

Prepared under Contract no. EX-76-A-01-2295, Task order 37.

TO AN ECONOMIST the study of economic development is in large part an investigation into the mechanics of capital formation. At least in theory, the output options open to a developing economy are more restricted in the case where possibilities for obtaining foreign exchange via trade or aid are relatively limited. Society's menu of choices is even easier to enumerate if it is further assumed that labor is surplus in the sense that labor supply is a non-binding constraint on economic development now and for some time to come. These conditions are roughly descriptive of the historical situation confronting some large underdeveloped nations wishing to industrialize rapidly; the U.S.S.R. in the thirties is a classic example. In such situations the key to economic growth is the capacity of the domestic capital goods sector. Increasing that capacity by ploughing back a high proportion of investment goods for purposes of self-reproduction will permit high consumption levels eventually, but not just in the near future. The reverse is true if, by bolting down a substantial percentage of investment goods there, the consumer goods sector is presently expanded. These thoughts underlie a very interesting model of economic development first propounded by the Soviet engineering economist G. A. Fel'dman in 1928 [7] 2 We are indebted to Professor Domar [6] for pointing out the significance of this model and for relating it to current growth theory as well as to the Soviet industrialization debate of the twenties. The same model has been independently formulated by the Indian statistician P. C. Mahalanobis [9] who places somewhat greater emphasis on making it operational enough to serve as a rough guide of sorts for Indian long term planning.3 In its simplest form this model splits an economy into two departments, investment and consumption. Investment goods are general ex ante and can be used to increase the capacity of either sector. But ex post, capital is specific to the

With climate change as prototype example, this paper analyzes the implications of structural uncertainty for the economics of low-probability, high-impact catastrophes. Even when updated by Bayesian learning, uncertain structural parameters induce a critical “tail fattening” of posterior-predictive distributions. Such fattened tails have strong implications for situations, like climate change, where a catastrophe is theoretically possible because prior knowledge cannot place sufficiently narrow bounds on overall damages. This paper shows that the economic consequences of fat-tailed structural uncertainty (along with unsureness about high-temperature damages) can readily outweigh the effects of discounting in climate-change policy analysis.

At high enough greenhouse gas concentrations, climate change might conceivably cause catastrophic damages with small but non-negligible probabilities. If the bad tail of climate damages is sufficiently fat, and if the coefficient of relative risk aversion is greater than one, the catastrophe-reducing insurance aspect of mitigation investments could in theory have a strong influence on raising the social cost of carbon. In this paper I exposit the influence of fat tails on climate change economics in a simple stark formulation focused on the social cost of carbon. I then attempt to place the basic underlying issues within a balanced perspective.

In textbook expositions of the equity-premium, riskfree-rate and equity-volatility puzzles, agents are sure of the economy's structure while growth rates are normally distributed. But because of parameter uncertainty the thin-tailed normal distribution conditioned on realized data becomes a thick-tailed Student-t distribution, which changes the entire nature of what is considered “puzzling” by reversing every inequality discrepancy needing to be explained. This paper shows that Bayesian updating of unknown structural parameters inevitably adds a permanent tail-thickening effect to posterior expectations. The expected-utility ramifications of this for asset pricing are strong, work against the puzzles, and are very sensitive to subjective prior beliefs—even with asymptotically infinite data. (JEL D84, G12)

By incorporating the probability distribution directly into the analysis, this paper proposes a new theoretical approach to resolving the perennial dilemma of being uncertain about what discount rate to use in cost-benefit analysis. A numerical example is constructed from the results of a survey based on the opinions of 2,160 economists. The main finding is that even if every individual believes in a constant discount rate, the wide spread of opinion on what it should be makes the effective social discount rate decline significantly over time. Implications and ramifications of this proposed “gamma-discounting” approach are discussed. (JEL H43)